SN2 versus SN2′ Competition

We have quantum chemically explored the competition between the SN2 and SN2′ pathways for X– + H2C=CHCH2Y (X, Y = F, Cl, Br, I) using a combined relativistic density functional theory and coupled-cluster theory approach. Bimolecular nucleophilic substitution reactions at allylic systems, i.e., Cγ=Cβ–Cα–Y, bearing a leaving-group at the α-position, proceed either via a direct attack at the α-carbon (SN2) or via an attack at the γ-carbon, involving a concerted allylic rearrangement (SN2′), in both cases leading to the expulsion of the leaving-group. Herein, we provide a physically sound model to rationalize under which circumstances a nucleophile will follow either the aliphatic SN2 or allylic SN2′ pathway. Our activation strain analyses expose the underlying physical factors that steer the SN2/SN2′ competition and, again, demonstrate that the concepts of a reaction’s “characteristic distortivity” and “transition state acidity” provide explanations and design tools for understanding and predicting reactivity trends in organic synthesis.


■ INTRODUCTION
Bimolecular nucleophilic substitution reactions at allylic systems bearing a leaving-group at the α-position give rise to a competition between the aliphatic S N 2 and allylic S N 2′ reaction channels (Scheme 1). For this class of substrates, the nucleophile, i.e., Lewis base, can directly attack either the αcarbon (S N 2) or the γ-carbon involving a concerted allylic rearrangement (S N 2′, also known as S N 2 prime). 1 This intrinsic competition can result in unwanted side products and hampers the applicability of these transformations in synthetic chemistry. Nevertheless, in the last years, the S N 2′ reaction has advanced into an important member of the chemical toolbox of synthetic chemists. Especially, the copper-catalyzed S N 2′ reaction has become a key synthetic methodology to forge new C−C bonds with good regio-and stereoselectivity. 2,3 Both experimental 4 and theoretical studies 5 have provided insights into the S N 2/S N 2′ competition. In general, the aliphatic S N 2 pathway is favored; however, the allylic S N 2′ can become dominant when an attack on the α-position is sterically retarded. Following this, the use of model substrates such as H 2 C CHCR 2 Y (e.g., R = alkyl group) presents an almost exclusive preference for the S N 2′ reaction. 6 Similarly, allylic rearrangements of propargylic systems (C γ C β −C α −Y) conveniently furnish allenes. 7 Despite these advances, the physical phenomena governing the preference of the S N 2/S N 2′ reaction channels are currently lacking in the literature. This ultimately thwarts the judicious tuning of the reactivity toward the desired pathway.
To this end, we have analyzed the reaction profiles of the S N 2, anti-S N 2′, and syn-S N 2′ reaction pathways of X − + H 2 C CHCH 2 Y with X, Y = F, Cl, Br, I, using relativistic density functional theory (DFT). We have also computed DLPNO-CCSD(T) reference data that confirm the reliability of our DFT approach. The archetypal substrate H 2 CCHCH 2 Y is an ideal model system to probe the competition between S N 2/S N 2′ and derive the intrinsic underlying physical factors and properties of the system that steer this competition. This study equips us with a systematic overview of reactivity trends over a wide range of reactivities and pathways, which can be extended to any substrate where the allylic system and the leaving-group are electronically coupled. The activation strain model (ASM) 8 of reactivity in conjunction with Kohn−Sham molecular orbital (KS−MO) theory 9,10 were employed to pinpoint the physical phenomena that control the competition between the aliphatic S N 2 and allylic S N 2′ pathway of the aforementioned reaction. In line with our previous work on the S N 2/E2 reaction, 11 the S N 2/ S N 2′ competition could be traced back to (i) the "characteristic distortivity" of the substrate, which is directly connected with the "transition state acidity" for each specific reaction pathway; (ii) the strength of the nucleophile, i.e., Lewis base, which enters into an acid−base-like interaction with the substrate; and (iii) the leaving-group capacity. Scheme 1. S N 2 and S N 2′ Pathways for Reactants X − + H 2 CCHCH 2 Y (X, Y = F, Cl, Br, I) Table 1. Energies Relative to the Reactants for All Stationary Points of the S N 2, Anti-S N 2′, and Syn-S N 2′ Pathways Following    Table 1. In all cases, the reaction proceeds via a double-well potential energy surface (PES), going from the reactant complex (RC) through a transition state (TS) towards the product complex (PC), which may ultimately dissociate into the separated products (P). Structural data of the stationary points for two representative reactions are shown in Figure 1. Note that the overall activation energy ΔE ‡ , that is, the energy difference between the TS and the infinitely separated reactants (X − and H 2 CCHCH 2 Y), can be negative if a substantially stabilized reactant complex is formed. For a more detailed discussion on the various types of reaction potential energy surfaces, see, for example, ref 12. Importantly, the computed trends in reactivity at ZORA-M06-2X/QZ4P//ZORA-OLYP/ QZ4P agree well with those calculated at the more accurate (TightPNO)DLPNO-CCSD(T)/CBS(3,4/def2)//ZORA-OLYP/QZ4P level (see Table 1).
Several interesting reactivity trends can be derived from the reaction profiles (Table 1). In the first place, in line with experimental findings, 4 for most of the studied systems, except for X, Y = F, there is a preference for the aliphatic S N 2 pathway (see also Figure 6a). 4 Second, of the two possible allylic S N 2′ pathways, that is anti-S N 2′ and syn-S N 2′, the anti-S N 2′ reaction pathway consistently goes with a lower activation energy than the syn-S N 2′ pathway (ΔΔE ‡ = −2.3 to −3.4 kcal mol −1 for anti-S N 2′ relative to syn-S N 2′ using DFT) regardless of the nucleophile and leaving-group combination. As such, we will limit further discussion solely to the comparison between the anti-S N 2′ and S N 2 reaction pathways. Third, the activation energy of all nucleophilic substitution reactions (S N 2, anti-S N 2′, and syn-S N 2′) increases when a weaker, i.e., less basic, anionic nucleophile X − is used going from F − to Cl − to Br − to I − . For example, the activation energy for the aliphatic S N 2 pathway increases going from ΔE ‡ = +0.7 to +24.1 to +28.7 to +36.2 kcal mol −1 upon going from X − = F − to Cl − to Br − to I − , when Y = F is the leaving-group. This is a manifestation of the reduced intrinsic nucleophilicity along this series. 11 Interestingly, our computations reveal that along the same series, the anti-S N 2′ activation energy rises to a larger extent than the S N 2 activation energy, inducing a switch in the preferred reaction pathway from anti-S N 2′ when the nucleophile is F − to S N 2 for nucleophiles Cl − , Br − , and I − (ΔΔE ‡ = +7.6, −1.1, −4.8, −5.3 kcal mol −1 for S N 2 relative to anti-S N 2′). Thus, in this series, the anti-S N 2′ The Journal of Organic Chemistry pubs.acs.org/joc Article dominates for the more basic halide X − = F − , with an activation energy that is 7.6 kcal mol −1 lower than that of the S N 2 pathway, whereas the S N 2 pathway prevails for the heavier, less basic halides, X − = Cl − , Br − , and I − . For the latter three nucleophiles, regardless of the leaving-group Y, the S N 2 pathway is always preferred, which is a direct result of their lower basicity (vide infra).
On the other hand, for any nucleophile X − , varying the leaving-group along Y = F, Cl, Br, and I significantly lowers all nucleophilic substitution activation energies. For example, the activation energy for the S N 2 pathway decreases from ΔE ‡ = +0.7 to −14.0 to −18.2 to −18.8 kcal mol −1 along Y = F, Cl, Br, and I, respectively, using nucleophile X = F − . Importantly, along the same series, the most favorable reaction pathway switches from anti-S N 2′ for Y = F to S N 2 for Y = Cl, Br, and I, because the activation energy of the latter reaction decreases more rapidly than that of the former reaction (e.g., ΔΔE ‡ = +7.6, −1.1, −4.8, −5.3 kcal mol −1 for S N 2 relative to anti-S N 2′; see Table 1). In the next section, the origin of these reactivity trends is further analyzed and rationalized on the basis of the activation strain model (ASM) 8 of reactivity in combination with quantitative Kohn−Sham molecular orbital (KS−MO) 9,10 theory.
Activation Strain Analyses. The results emerging from utilizing the activation strain model (ASM) of reactivity for the representative S N 2 and anti-S N 2′ reactions of X − and H 2 C CHCH 2 Y (X, Y = F, Cl) are summarized in Figures 2−5 (see the Supporting Information Figure S1 for all activation strain diagrams). The ASM is a fragment-based approach in which the potential energy surface (PES) can be described with respect to, and understood in terms of, the characteristics of the reactants, i.e., the nucleophile and substrate. This analysis method decomposes the total electronic energy (ΔE) into two distinct terms, that is, the strain energy (ΔE strain ) and the interaction energy (ΔE int ). The strain energy is the penalty that needs to be paid to deform the individual reactants to react and the interaction energy accounts for all mutual interactions between the deformed reactants along the entire reaction coordinate, in this case, defined as the IRC projection onto the C α ···Y stretch. 11,13 This is a critical reaction coordinate that is intimately connected to the progress of nucleophilic substitution reactions on going from the reactant complex to the transition state to the product complex.
In Figure 2, we show how changing the anionic nucleophile X − , panels (a) and (c), and the leaving-group Y, panels (b) and (d), affect the reactivity of both the aliphatic S N 2 and allylic S N 2′ pathways. Changing the nucleophile from F − to Cl − leads, in line with its decreased basicity, to a significant loss of stabilizing interaction energy between the nucleophile and substrate, and hence results in an increase of the activation energy ( Figure  2a,c). The strain energy, in contrast, is hardly affected by changing the strength of the nucleophile because it is mainly determined by the strength of the C α −Y bond, which remains constant. Therefore, the strain energy is not responsible for the reduced reactivity of the nucleophilic substitution reactions. The Journal of Organic Chemistry pubs.acs.org/joc Article A weaker nucleophile, i.e., going from F − to the weaker Lewis base Cl − , results in a weakening of the acid−base-like HOMO X − −LUMO substrate interaction with the substrate over the entire course of the reaction. This loss of HOMO−LUMO interaction originates from the fact that the halide X − np atomic orbital (AO) decreases in energy from F − to I − , which, consequently, increases the corresponding HOMO X − −LU-MO substrate orbital energy gap (Figure 3; see ref 14 for a detailed discussion of the difference in the AO orbital energies of halogen atoms and halide anions).
In contrast, changing the leaving-group from Y = F to Cl promotes both the S N 2 and S N 2′ reactivities by reducing the destabilizing strain energy (Figure 2b,d). The interaction energy, however, does not change upon altering the leavinggroup and hence is not responsible for the observed enhanced reactivity. The less destabilizing strain originates directly from the weaker carbon−leaving-group bond descending in Group 17 (i.e., halogens), rendering it easier to break, thus requiring less energy. 15 Notably, we recently found that when going down Group 17, the carbon−halogen bond, i.e., carbon−leavinggroup bond, does not become weaker because of the decreasing electronegativity difference but, instead, due to the increasing steric (Pauli) repulsion across the C−Y bond for the larger halogen atoms. 16 To analyze the competition between S N 2 and S N 2′, we collect in Figure 4 four panels showing the aliphatic S N 2 and allylic S N 2′ pathways of the model reactions: (a) F − + H 2 CCHCH 2 F, (b) F − + H 2 CCHCH 2 Cl, (c) Cl − + H 2 CCHCH 2 F, and (d) Cl − + H 2 CCHCH 2 Cl. The nature of the nucleophile changes in the vertical direction, whereas the leaving-group is altered in the horizontal direction. Several characteristic trends for the S N 2 (attack at the σ*) and S N 2′ (attack at the π*) pathways can be derived from the computed activation strain diagrams (ASDs). For all studied reactions, the aliphatic S N 2 reaction pathway goes with a lower strain energy than the allylic S N 2′ analog (see also Figure S1). This difference is the direct result of the required allylic rearrangement that occurs only along the S N 2′ pathway.
During both reactions, the C α −Y bond is being broken; however, for the S N 2′ pathway, there is a concurrent reorganization of the allylic backbone, going from H 2 C γ  C β HC α H 2 ···Y to H 2 C γ C β HC α H 2 ···Y. Resultingly, the "characteristic distortivity" along the S N 2 pathway is inherently lower than along the corresponding S N 2′ pathway. Notably, we have observed a similar relationship between structural deformation and reaction pathway when studying the S N 2/E2 competition, 11 where the S N 2 pathway (one bond-breaking event in the substrate) goes with intrinsically less structural deformation, i.e., characteristic distortivity, than the E2 pathway (two bondbreaking events in the substrate). Importantly, the strain curves at the end of the nucleophilic substitution reactions, thus close to the product complex, begin to converge to nearly the same energy. This is because the product complexes of both the S N 2 and S N 2′ pathways are structurally similar.
A same product molecule is formed and only the site at which the leaving-group coordinates is different (see product complexes in Figure 1). This phenomenon of converging strain curves in the product complex contrasts with the S N 2/E2 competition, in which the E2 reaction features, along the entire reaction pathway, an increasingly more destabilizing strain energy, as it forms a PC composed of entirely different product molecules than the S N 2 reaction. 11 At the same time, the characteristic distortivity also has a profound effect on the electronic structure of the substrate (Figures 5 and 6b). In our reaction systems, a higher characteristic distortivity, i.e., more deformation of the substrate, gives rise to a lower-energy LUMO in the substrate. The reason for this is that the LUMO of the substrate has destabilizing antibonding character in the C α −Y and C γ C β bonds and stabilizing bonding character in the C β −C α bond ( Figure 5). The elongation of the C α −Y bond found during both the S N 2 and S N 2′ reactions reduces the antibonding overlap in this bond, resulting in a stabilization of the LUMO orbital energy. Additionally, the allylic rearrangement along the S N 2′ pathway induces a stretch of the C γ C β bond and a contraction of the C β −C α , which results in less destabilizing antibonding character in the C γ C β bond and more bonding character in the C β −C α bond. Both geometrical deformations lead to an additional stabilization of the LUMO of the substrate during the S N 2′ reaction. Note that at the beginning of the reaction almost no deformation has taken place, and hence the LUMO energy difference between the S N 2 and S N 2′ is very small ( Figure S2). Moreover, as previously discussed, the product complexes of both the S N 2 and S N 2′ pathways are comparable in structure, which causes the LUMO energies of the different reaction pathways to converge at the end of the reaction. This will, as discussed below, have direct implications on the observed reactivity trends when the transition states appear to be very early or late on the reaction coordinate.
Altogether, these findings allow us to translate the interaction energy emerging from our activation strain analyses, in analogy with our previous work on the S N 2/E2 competition, 11 into fundamental concepts that are intrinsically based on the strength of the Lewis acid (substrate) and Lewis base (nucleophile). It is well-known from acid−base chemistry that a more basic Lewis base (high-energy HOMO) will interact more strongly with a more acidic substrate (low-energy LUMO). 17 We, therefore, use the, previously introduced by us, 11 concept of "transition state acidity", that is, the effective acidity of a deformed substrate in the transition state. As discussed earlier, the S N 2 pathway goes with a less acidic substrate (higher-energy LUMO) than the The Journal of Organic Chemistry pubs.acs.org/joc Article S N 2′ pathway (lower-energy LUMO). Therefore, the S N 2′ pathway can dominate the S N 2 pathway in the limit of a very strong interaction (stronger Lewis base), which we have observed for the reactions in which X, Y = F (Figures 4a and  6a). Changing the nucleophile from X − = F − to Cl − has a profound effect on the preferred reaction pathway, shifting the preference from S N 2′ for F − (Figure 4a) to S N 2 for Cl − ( Figure  4c). This is a direct consequence of the less stabilizing HOMO− LUMO interaction between nucleophile and substrate as we go from the stronger base F − to the weaker base Cl − . The weaker interaction in the case of the latter is no longer able to overcome the higher strain associated with the higher characteristic distortivity along the S N 2′ pathway and hence results in a preference for the S N 2 pathway ( Figure 6b). Likewise, for Y = Cl as leaving-group, going from X = F − (Figure 4b) to X = Cl − (Figure 4d), the preference for S N 2 increases (ΔΔE ‡ = −2.0 to −5.7 kcal mol −1 for S N 2 relative to anti-S N 2′); however, since X = F − follows already the S N 2 pathway, no switch in mechanism is observed. Note that, in the case of the weaker nucleophile Cl − , the position of the transition states shifts to a later point on the reaction coordinate because of the less stabilizing and more shallow interaction curve. The occurrence of the TS at a later stage of the reaction causes a smaller difference in LUMO energy between the aliphatic S N 2 and allylic S N 2′ pathways and hence a smaller difference in "transition state acidity" (see also Figure  S2). On the other hand, increasing the leaving-group ability, from Y = F to Cl (Figure 4a−d), shifts the position of the transition states to an early position on the reaction coordinate, especially for the S N 2′ pathway. At these early stages of the reaction, almost no substrate deformation has taken place and hence no stabilization of the LUMO. This, ultimately, yields no apparent difference in "transition state acidity" between the pathways, and thus, we observe erosion of the S N 2′ preference shifting to the less distortive S N 2 pathway. Our model can also explain the effect of solvation on the S N 2 versus S N 2′ competition. The localized charge density on the anionic nucleophile (Lewis base) is highly stabilized upon   Figure S2 for quantitative data on the relationship between characteristic distortivity and electronic structure.
The Journal of Organic Chemistry pubs.acs.org/joc Article solvation, which leads to a stabilization of the HOMO of X − (weaker nucleophile). Thus, the HOMO−LUMO interaction (acid−base-like interaction) between the Lewis base and substrate is weakened by solvation. 11c The weaker interaction ultimately causes a shift to the less distortive S N 2 pathway. To showcase this fundamental effect, we have computed the S N 2 and anti-S N 2′ activation barriers of all our systems with the inclusion of solvation simulated with COSMO (dichloromethane). As expected, as a result of solvation, all reaction barriers increase significantly and follow the less distortive S N 2 pathway (Table S2), which is a direct consequence of the weakening of the Lewis-basic nucleophiles. For example, by going from the gas phase to solution, the X, Y = F system switches from S N 2′ to S N 2. Note that these effects will be even more pronounced when the polarity of the solvent increases. 11c Lastly, we investigated the S N 2/S N 2′ competition of more commonly used nucleophiles MeO − , MeS − , MeSe − , and MeTe − with C 2 H 5 F as a substrate to test our model (Table S3). As discussed earlier, strong nucleophiles will have a more favorable interaction with the substrate than weak nucleophiles and, therefore, the former will be able to overcome the characteristic high distortivity accompanied with the S N 2′ reaction. Hence, based on the strength of the nucleophile, which is associated with the energy of the HOMO, one can anticipate the preferred reaction pathway. By going down a group in the periodic table, the HOMO energy becomes stabilized, resulting in a lower nucleophilicity along MeO − , MeS − , MeSe − , and MeTe − . As expected, the S N 2′ preference erodes on going from MeO − to MeS − , MeSe − , and MeTe − (ΔΔE ‡ = +9.1, +6.1, +2.9, +1.6 kcal mol −1 for S N 2 relative to anti-S N 2′). The weakest nucleophile in this series still has a preference for the S N 2′ pathway as a result of the intrinsic higher reactivity of Group 16 (chalcogens) compared to Group 17 (halogens) in the periodic table.

■ CONCLUSIONS
Bimolecular nucleophilic substitution at archetypal allylic substrates X − + H 2 CCHCH 2 Y (X, Y = F, Cl, Br, I) can follow two distinct mechanistic pathways: aliphatic S N 2 or allylic S N 2′ substitution. The aliphatic S N 2 pathway is in general favored over the allylic S N 2′ mechanism. For our studied systems, we found that the latter only dominates in the case of a strong nucleophile (X − = F − ) in combination with a poor leaving-group (Y = F). Both mechanistic pathways are accelerated as the Lewis basicity of the anionic nucleophile increases, along X − = I − to F − , and the carbon−leaving-group (C−Y) bond becomes weaker, along Y = F to I. These and other insights emerge from our detailed quantum chemical analyses based on relativistic DFT.
Our activation strain analyses reveal that a stronger, more Lewis-basic nucleophile X − (e.g., going from Cl − to F − ) lowers the activation energy for both the S N 2 and S N 2′ pathways, because of a more stabilizing acid−base-like HOMO X − − LUMO substrate interaction with the substrate over the entire course of the reaction. A leaving-group Y possessing a weaker C−Y bond in the substrate (e.g., going from C−F to C−Cl) also lowers the activation energy for both the S N 2 and S N 2′ pathways, because a less destabilizing activation strain needs to be overcome to break such a weaker carbon−leaving-group bond.
In analogy to the previously studied S N 2/E2 competition, 11 the propensity of the Lewis-basic nucleophile to follow an S N 2 or S N 2′ pathway is found to be steered by the distinct structural deformation of the substrate during the course of the reaction in combination with the nature of the Lewis base and the leavinggroup. The allylic S N 2′ pathway (C−Y bond breaking and allylic rearrangement in the substrate) is characterized by a higher "characteristic distortivity" than the aliphatic S N 2 pathway (only C−Y bond breaking in the substrate). The higher characteristic distortivity of the S N 2′ pathway is associated with a higher activation strain, which contributes to the S N 2′ activation energy being higher than the S N 2 one.
But the higher distortivity of the S N 2′ pathway also stabilizes the LUMO (lower-energy LUMO) of the substrate and furnishes a substrate with an effectively higher TS acidity. In the case of strong Lewis-basic nucleophiles (X − = F − in our case), this can lead to sufficiently stabilizing HOMO−LUMO interaction between nucleophile and substrate that can overcome the higher activation strain of the S N 2′ pathway, making it the dominant mechanism over S N 2. For the weaker Lewis bases (X − = Cl − , Br − , I − ), and thus also for (strongly) solvated Lewis bases, the HOMO−LUMO interaction is not strong enough to overcome the higher activation strain of the allylic S N 2′ pathway and, thus, the less distortive aliphatic S N 2 substitution emerges as the dominant pathway. Our present work demonstrates the more general applicability of the concepts of "characteristic distortivity" and "transition state acidity" to not only explain but also predict reactivity trends of fundamental organic reactions. Figure 6. Schematic summary of the S N 2/S N 2′ competition. (a) Reaction pathway preference for X − and H 2 CCHCH 2 Y with X, Y = F, Cl, Br, and I. (b) "Characteristic distortivity" (destabilizing) and "transition state acidity" (stabilizing) of the aliphatic S N 2 and allylic S N 2′ reaction pathways, where the characteristic distortivity (deformation; red) is always higher along the S N 2′ pathway than the S N 2. However, this can be overcome using strong Lewis bases (nucleophiles), by the corresponding transition state acidity (lowerlying LUMO; green).
The Journal of Organic Chemistry pubs.acs.org/joc Article ■ COMPUTATIONAL METHODS Computational Details. All density functional theory (DFT) calculations were performed using the Amsterdam Density Functional (ADF2018.105) software package. 18 The generalized gradient approximation (GGA) exchange−correlation functional OLYP was used for all geometry optimizations, which consists of the optimized exchange (OPTX) functional proposed by Handy and co-workers 19a and the Lee−Yang−Parr (LYP) correlation functional. 19b Our benchmark studies have shown that OLYP gives accurate nucleophilic substitution stationary point geometries. 20 Scalar relativistic effects are accounted for using the zeroth-order regular approximation (ZORA). 21 The basis set used, denoted QZ4P, is of quadruple-ζ quality for all atoms and has been improved by four sets of polarization functions. 22 This large basis set is required for small anionic species (e.g., F − ). All solution-phase calculations used COSMO to simulate bulk solvation. For these calculations, the optimized stationary points in the gas phase were fully reoptimized at COSMO(DCM)-ZORA-OLYP/QZ4P. 23 The accuracies of the fit scheme (Zlm fit) and the integration grid (Becke grid) were, for all calculations, set to VERYGOOD. 24 No symmetry constraints were used for all computations. All calculated stationary points have been verified by performing a vibrational analysis calculation, 25 to be energy minima (no imaginary frequencies) or transition states (only one imaginary frequency). The character of the normal mode associated with the imaginary frequency of the transition state has been inspected to ensure that it is associated with the reaction of interest. The stationary point energies have been refined by performing single points at ZORA-M06-2X 26 /QZ4P, using ADF, 18 as well as (TightPNO)DLPNO-CCSD(T)/CBS(3,4/def2), 27 using ORCA 5.0.1, 28 on the ZORA-OLYP/QZ4P geometries. The potential energy surfaces of the studied bimolecular nucleophilic substitution reactions were obtained by means of intrinsic reaction coordinate (IRC) calculations, which confirmed the correct transition state of interest. 29 The IRC calculations were analyzed using the PyFrag 2019 program. 30 The optimized structures were illustrated using CYLview. 31 Activation Strain Model of Reactivity. The activation strain model (ASM) of chemical reactivity, 8 also known as the distortion/ interaction model, 32 is a fragment-based approach in which the potential energy surface (PES) can be described with respect to, and understood in terms of the characteristics of, the reactants. It considers the rigidity of the reactants and to which extent they need to deform during the reaction, plus their capability to interact with each other as the reaction proceeds. With the help of this model, we decompose the gas-phase total energy, ΔE(ζ), into the strain and interaction energy, ΔE strain (ζ) and ΔE int (ζ), respectively, and project these values onto the reaction coordinate ζ (eq 1).
In this equation, the strain energy, ΔE strain (ζ), is the penalty that needs to be paid to deform the reactants from their equilibrium to the geometry they adopt during the reaction at the point ζ of the reaction coordinate. On the other hand, the interaction energy, ΔE int (ζ), accounts for all of the chemical interactions that occur between these two deformed reactants along the reaction coordinate. Note that at the position along the reaction coordinate where the destabilization of the strain terms increases with the same slope as the stabilization of the interaction energy term increases, i.e., dΔE strain (ζ)/dζ = −dΔE int (ζ)/ dζ, the derivative of the total energy ΔE(ζ) with respect to the reaction coordinate is zero (dΔE(ζ)/dζ = 0). 8 At this point, the reaction profile reaches either a maximum (transition state) or a minimum (reactant complex or product complex).
In the herein presented activation strain and accompanied energy decomposition diagrams, the intrinsic reaction coordinate (IRC) is projected onto the carbon−leaving-group (C α ···Y) distance. This critical reaction coordinate undergoes a well-defined change during the reaction from the reactant via the transition state to the product. 11,13 ■ ASSOCIATED CONTENT
Additional computational results and Cartesian coordinates, energies, and the number of imaginary frequencies of all stationary points (PDF)